Properties

Label 6897.f
Number of curves $1$
Conductor $6897$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 6897.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6897.f1 6897a1 \([0, -1, 1, -282, -1915]\) \(-1404928/171\) \(-302936931\) \([]\) \(5720\) \(0.36240\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 6897.f1 has rank \(1\).

Complex multiplication

The elliptic curves in class 6897.f do not have complex multiplication.

Modular form 6897.2.a.f

sage: E.q_eigenform(10)
 
\(q + 2 q^{2} - q^{3} + 2 q^{4} - 3 q^{5} - 2 q^{6} + 5 q^{7} + q^{9} - 6 q^{10} - 2 q^{12} - 2 q^{13} + 10 q^{14} + 3 q^{15} - 4 q^{16} + q^{17} + 2 q^{18} + q^{19} + O(q^{20})\) Copy content Toggle raw display